The rules serve the DM, not vice versa
A DM can't "break rules" because DMs don't obey the rules in the first place. In 5e the rules are DM's tool for running games. The DM is in charge, not the rules. The DMG explicitly says this a couple of times, as well as other sourcebooks:
Rules enable you and your players to have fun at the table. The rules serve you, not vice versa.
DMG page 235
You basically answered your own question by saying that
The DM has the power to break and add rules
With only one correction that DM don't "break" the rules, she removes or changes them instead. The DM is the final authority:
One rule overrides all others: the DM is the final authority on how the rules work in play.
XGtE page 5
However, if players don't have fun, that means the DM does their job poorly (and it's OK for a new DM). Maybe your DM miscalculated things, or these 800 gp were intended for the whole party, not a one player.
In this case, communicate with them. Your DM can't read minds, apparently. Ask questions ("Why do I have only 80 gp and others have 800?") and give them feedback accenting your own experience ("I feel overshadowed by other players when choosing my starting equipment, and this is not fun").
Keep in mind, that Dungeons and Dragons is not a competitive game, it's a cooperative one. Neither the DM nor other players can "win" the game over each other. Everyone is a winner, providing everyone is having fun. But if one player is not, the whole table "loses", so to say.